Contrary to reports that Lopez asked for a $2 million raise to continue judging the Fox reality show for a third season, the source says that Fox did approach Lopez with a "comparable offer to last year's salary" for next season, but it was never countered nor negotiated by her team.

For her first season on the show, Lopez earned $15 million. And she did get a raise for her second season, the source says, because Fox understood the value she brought to the series. Her second year salary was $20 million plus bonuses, says the source. PEOPLE reached a Fox rep who had no comment.

Regarding her decision to leave, the source says it was a difficult one, and was informed by the star's interest in focusing on her family, film career and other creative ventures, including her fashion business.

"I could do Idol for the rest of my life," she said at the time, "but that would be giving up a bunch of other things ... I have my movies and my music and my this and my that. It all kind of worked together for a while, but then it gets more complicated."

Still, she said at the time, "I've never felt so much a part of a family of something I've been working on as I did with Idol. I didn't know I'd be moved so emotionally by working on the show and working with the contestants."